Shuts down for 2 weeks, then wakes

i have an IPod Classic 120. It's developed a strange quirk where it will play fine for months, then suddenly shut off completely and there's no way I can wake it up. After letting it sit. Sometimes for almost 2 weeks, suddenly I'm able to turn it on and it will work fine for several weeks / months. This has happened several times. Can this be repaired and approx. how much?